Fixed Grid Numerical Models for Solidification and Melting of Phase Change Materials (PCMs)

Phase change materials (PCMs) are classified according to their phase change process, temperature, and composition. The utilization of PCMs lies mainly in the field of solar energy and building applications as well as in industrial processes. The main advantage of such materials is the use of latent heat, which allows the storage of a large amount of thermal energy with small temperature variation, improving the energy eciency of the system. The study of PCMs using computational fluid dynamics (CFD) is widespread and has been documented in several papers, following the tendency that CFD nowadays tends to become increasingly widespread. Numerical studies of solidification and melting processes use a combination of formulations to describe the physical phenomena related to such processes, these being mainly the latent heat and the velocity transition between the liquid and the solid phases. The methods used to describe the latent heat are divided into three main groups: source term methods (E-STM), enthalpy methods (E-EM), and temperature-transforming models (E-TTM). The description of the velocity transition is, in turn, divided into three main groups: switch-o methods (SOM), source term methods (STM), and variable viscosity methods (VVM). Since a full numerical model uses a combination of at least one of the methods for each phenomenon, several combinations are possible. The main objective of the present paper was to review the numerical approaches used to describe solidification and melting processes in fixed grid models. In the first part of the present review, we focus on the PCM classification and applications, as well as analyze the main features of solidification and melting processes in dierent container shapes and boundary conditions. Regarding numerical models adopted in phase-change processes, the review is focused on the fixed grid methods used to describe both latent heat and velocity transition between the phases. Additionally, we discuss the most common simplifications and boundary conditions used when studying solidification and melting processes, as well as the impact of such simplifications on computational cost. Afterwards, we compare the combinations of formulations used in numerical studies of solidification and melting processes, concluding that “enthalpy–porosity” is the most widespread numerical model used in PCM studies. Moreover, several combinations of formulations are barely explored. Regarding the simulation performance, we also show a new basic method that can be employed to evaluate the computing performance in transient numerical simulations

Theoretical and numerical analysis on phase change materials (PCM): A case study of the solidification process of erythritol in spheres

Phase change materials (PCM) present great potential for energy efficiency gains in thermal systems by storing solar energy or waste heat in industrial processes. This is due to the great amount of energy stored per mass unit within a small temperature range. In this paper we focus, by means of the numerical investigation, on the solidification process of the PCM erythritol in spheres, having 10, 20, 30 and 40 mm diameter, under wall temperatures of 10, 15, 20, 25, 30 and 40 K below the phase change temperature of the material. The problem is considered two-dimensional in geometry and transient in time. The numerical model here adopted consists of mass, momentum, energy and volume fraction equations. The results have been initially validated by comparison with data found in literature. Afterwards, analysis of the convective streams on the liquid PCM, liquid fraction, heat flux in the sphere wall and total solidification times have been widely illustrated. The liquid fraction suffers a sharp reduction at the beginning of the solidification process due to the high heat flux at the initial times. As the solid layer adjacent to the shell increases, it causes an augmentation of thermal resistance, significantly reducing the heat flux. The shape of the curve representing the solid fraction shows similarity with the S-curve pattern of solidification. The total solidification time proved to be dependent on both the diameter length and the temperature difference DT (between phase change material and wall temperature), being its influence reduced for lower temperature values. Finally, the liquid fraction results, as a function of Fourier and Stefan numbers, have been employed to amend a dimensionless correlation found in literature

Phase change materials (PCM) for building envelope applications: A review of numerical models

Phase Change Materials (PCM) present a great potential for energy efficiency gains in thermal systems, e.g. by storing solar energy in buildings or heat loads in industrial processes. This is because a great amount of energy can be stored per mass unit within a small temperature range. Significant applications of this peculiar characteristic of PCM regard the effective adoption of macro-encapsulated PCM into building envelopes. Several studies on this topic tend to be limited to a sort of “material selections” on PCM and a lack of systematic analysis has consequently emerged. In order to guarantee an effective use coupled with economic feasibility, a deep understanding of the phase transition phenomenon is needed. The study of PCM using computational fluid dynamics (CFD) is documented in several works, in accordance with the current trend of CFD to become increasingly widespread. Numerical studies on solidification and melting processes use a combination of formulations to describe the physical phenomena related to such processes, mainly the latent heat and the velocity transition between the liquid and the solid phases. The methods used to describe the latent heat are divided in three main groups: (i) source term methods (E-STM), (ii) temperature transforming models (E-TTM) and (iii) enthalpy methods (E-EM). The description of the velocity transition is in turn divided in three main groups: (i) switch-off method (SOM), (ii) source term method (STM) and (iii) variable viscosity method (VVM). In this context, the main objective of the present paper is to review the numerical approaches used to describe solidification and melting processes